Abstract
We define a Floer-homology invariant for knots in an oriented three-manifold, closely related to the Heegaard Floer homologies for three-manifolds defined in an earlier paper. We set up basic properties of these invariants, including an Euler characteristic calculation, and a description of the behavior under connected sums. Then, we establish a relationship with HF+ for surgeries along the knot. Applications include calculation of HF+ of three-manifolds obtained by surgeries on some special knots in S3, and also calculation of HF+ for certain simple three-manifolds which fiber over the circle.
Original language | English (US) |
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Pages (from-to) | 58-116 |
Number of pages | 59 |
Journal | Advances in Mathematics |
Volume | 186 |
Issue number | 1 |
DOIs | |
State | Published - Aug 1 2004 |
All Science Journal Classification (ASJC) codes
- Mathematics(all)